Fast and Robust Full Quadrature Triangular Elements for Thin Plates/Shells With Large Deformations and Large Rotations

Abstract

A new formulation for plates/shells with large deformations and large rotations is derived from the principles of continuum mechanics and calculated using the absolute nodal coordinate formulation (ANCF) techniques. A class of triangular elements is proposed to discretize the plate/shell formulation, which does not suffer from shear locking or membrane locking issue, and full quadrature can be performed to evaluate the integrals of each element. The adaptability of triangular elements enables the current approach to be applied to plates and shells with complicated shapes and variable thicknesses. The discretized mass matrix is constant, and the elastic force and stiffness matrix are polynomials of the generalized coordinates with constant coefficients. All the coefficients can be evaluated accurately beforehand, and numerical quadrature is not required in each time step of the simulation, which makes the current approach superior in numerical efficiency to most other approaches. The accuracy, robustness, and adaptability of the current approach are validated using both finite element benchmarks and multibody system standard tests.